helm/software/matita/tests/paratest.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "nat/plus.ma".
  16
  17 ntheorem foo:
  18    ((λx.x + 0 = x) ?) →
  19    ((λx,y.x + S y = S (x + y)) ? ?) →
  20    ((λx,y.y + x = x + y) ? ?) →
  21    ∀x. ((λz. x + x = z + S z) ?).
  22 ##[ #H; #H1; #H2; #x; nnormalize in H H1 H2 ⊢ %; nauto by H, H1, H2.